2001/03/06 by Yakov Itin · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Classical mechanics #Current (fluid) #Mathematical physics #Numerical methods for differential equations #Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Statistical physics #Theoretical physics #Thermodynamics #gr-qc
paper · pdf · doi:10.1142/s0217751x02011928
22 pages, 3 figures
arxiv created 2001/03/06 · openalex publication_date 2002/08/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The obstruction for the existence of an energy-momentum tensor for the gravitational field in GR is connected with vanishing of first order invariants in (pseudo) Riemannian geometry. This specific geometric property is not valid in alternative geometrical structures 1,2 . A parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields ϑ a is considered. A general 3-parameter class of global Lorentz invariant teleparallel models is considered. It includes a 1-parameter subclass of models with the Schwarzschild coframe solution (generalized teleparallel equivalent of gravity) 3 . By introducing the notion of a 3-parameter conjugate field strength F linear in the strength C a = dϑ a the coframe Lagrangian is rewritten in the Maxwell-Yang-Mills form L = 1/2F a ∧ C a . The field equation turns out to have a form d * F a = T a completely similar to the Maxwell field equation. By applying the Noether procedure, the source 3-form T a is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source T a of the coframe field is interpreted as the total conserved energy-momentum current of the coframe field and matter 4 . The energy-momentum tensor is defined as a map of the module of current 3-forms into the module of vector fields 5 . Thus an energy-momentum tensor for the coframe is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in the standard GR. The result is: The standard GR has a neighborhood of viable models with the same Schwarzschild solutions. These models however have a better Lagrangian behavior and produce an invariant energy-momentum tensor.